How to Use HFM for Asymmetric MDS

Naohito Chino
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Naohito Chino: Aichi Gakuin University, Emeritus Professor

Chapter Chapter 5 in Structure and Dynamics of Asymmetric Interactions, 2025, pp 123-142 from Springer

Abstract: Abstract In this sectionMultidimensional scaling (MDS) we shall introduce HFMHermitian Form Model (HFM) for the analysis of asymmetric (dis)similarity matrix, which was proposed by Chino and Shiraiwa (Chino and Shiraiwa in Behaviormetrika 39:127–165, 1993). Let us first suppose that we have an observedAsymmetric Similarity Matrix (ASM) asymmetric similaritySimilarity (similarities) matrix $${\varvec{S}} = \left[ {{\varvec{s}}_{{{\varvec{jk}}}} } \right]$$ S = s jk , whose element $${\varvec{s}}_{{{\varvec{jk}}}}$$ s jk denotes the intensity of the similarity from object j to object k among N objects. Therefore, matrix S is N by N, and is in general asymmetric. We shall hereafter abbreviate the Asymmetric Similarity MatrixAsymmetric Similarity Matrix (ASM) as ASM.

Date: 2025
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DOI: 10.1007/978-981-97-8269-7_5

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